Computational geometry deals with basic geometric objects such as points, line segments, polygons, and polyhedra, and aims to develop efficient algorithms and data structures for solving problems by figuring out the geometric, combinatorial, and topological properties of the objects. It has provided numerous methods and algorithms to solve geometric problems in application areas efficiently, such as computer graphics, robotics, geographic information systems, computer vision, and computational biology.
The traditional geometric algorithms, however, are not adequate for real-world data because they are not designed to handle imprecise and uncertain data and therefore they may return a wrong answer due to the imprecision or uncertainty of data.
This talk will provide an introduction to recent results of computational geometry on real-world data and open questions.

In shape matching, we are given two geometric objects and we compute their distance according to some geometric similarity measure. The Fréchet distance is a natural distance function for continuous shapes such as curves and surfaces, and is deﬁned using reparameterizations of the shapes.

The discrete Fréchet distance is a variant of the Fréchet distance in which we only consider vertices of polygonal curves. In this talk, we consider the problem of computing the discrete Fréchet distance between two polygonal curves when their vertices are imprecise, and describe efficient algorithms for the problem.